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If lines k and j are in the xy coordinate plane, is the

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If lines k and j are in the xy coordinate plane, is the [#permalink] New post 29 Sep 2009, 00:21
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If lines k and j are in the xy–coordinate plane, is the slope of line k greater than the slope of line j ?

(1) The x-intercept of line k is greater than the x-intercept of line j
(2) Lines k and j intersect at (7, 2)
[Reveal] Spoiler: OA

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Re: xy–coordinate plane [#permalink] New post 29 Sep 2009, 04:26
I get B but I am not sure. OA pls?
Following is the reasoning:
stmt 1: we just have two points on the x-axis. we can draw many lines via these two points and having different slopes. Insuff.

stmt2: we have the intersection point in the first quadrant. Now, draw a line perpendicular from (7,2) to the x-axis. This will be a vertical line. Now select two points on the axis just to right and left of (7,0) on x-axis. Let these points be the x-intercepts of the lines. Now the slope of line with a greater x-intercept say, (7.0001, 0 ) will always be -ve [in order to intersect (7,2)] and the slope of the line with a smaller x-intercept say (6.9999, 0 ) will always be +ve [in order to intersect (7,2)]

Suff.
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Re: xy–coordinate plane [#permalink] New post 29 Sep 2009, 07:01
Approach of economist is nice. Lets do it more mathematically.
1)insuff. No need to explain.
2)insuff. No need to explain.

together
line k=> y=mx+n
line j=> y=tx+y
we know from 1 that n is greater than y. And we know from 2 that they are intersecting at point (7,2).
That makes
2=7m+n
2=7t+y
7m+n=7t+y
7m+n<7t+n
7m<7t
m<t

SUFF.
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Re: xy–coordinate plane [#permalink] New post 29 Sep 2009, 07:14
Maliyeci,

I have two questions -

In y = mx + b equation, m = slope and b is the Y intercept. From your represenation, how can we say that

maliyeci wrote:
we know from 1 that n is greater than y.


when variables n and y are the Y intercepts. Not X intercepts.

Can you please explain how you made this Inequality based on n > y(assuming y intercepts of L > y intercept of K). I am confused. :roll:

maliyeci wrote:
7m+n<7t+n
7m<7t
m<t
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Re: xy–coordinate plane [#permalink] New post 29 Sep 2009, 07:24
IMO E. We need more information to find the answer.
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Re: xy–coordinate plane [#permalink] New post 29 Sep 2009, 07:36
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mrsmarthi wrote:
Maliyeci,

I have two questions -

In y = mx + b equation, m = slope and b is the Y intercept. From your represenation, how can we say that

maliyeci wrote:
we know from 1 that n is greater than y.


when variables n and y are the Y intercepts. Not X intercepts.

Can you please explain how you made this Inequality based on n > y(assuming y intercepts of L > y intercept of K). I am confused. :roll:

maliyeci wrote:
7m+n<7t+n
7m<7t
m<t

I beg your pardon for the intercepts. Yes you are rigth. I gave the Y intercept. The x intercepts are respectively;
-n/m and -y/t
But they are sufficient to find an answer.
That is the solution.
7m+n=2
n=2-7m
n/m=2/m-7
same as for the other
y/t=2/t-7
since -n/m is greater than -y/t; y/t is greater than n/m
so
2/m-7>2/t-7
2/m>2/t
so we can find the solution
C is suff.
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Re: xy–coordinate plane [#permalink] New post 29 Sep 2009, 08:16
Yes....this is correct. But with a small correction.

maliyeci wrote:
since -n/m is greater than -y/t; y/t is greater than n/m ==> n/m < y/t
so
2/m-7<2/t-7
2/m<2/t
so we can find the solution
C is suff.
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Re: xy–coordinate plane [#permalink] New post 29 Sep 2009, 08:35
Excellent explanation maliyeci....you are a God in quant :)
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Re: xy–coordinate plane [#permalink] New post 03 Oct 2009, 12:27
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Sorry to disappoint you guys, but seems that the answer should be E.

First of all to solve this question think that the best way is graphic approach:

We all agree that (1) and (2) alone are not sufficient.

Lets combine --> draw only X-axis. k intercept is greater than j intercept --> k intercept (k1) point right to j intercept point (j1) --> Interception of lines is above X-axis (point 7;2) --> it will give us only three possible ways to draw the lines:
A. j has negative slope, k has negative slope --> slope of k>slope of j, (because j is closer to vertical line);
B. j has positive slope, k has negative slope --> slope of k<slope of j;
C. j has positive slope, k has positive slope --> slope of k>slope of j, (because k is closer to vertical line);

So (1)+(2) not sufficient. Answer E.

BUT the way you were solving also should get E:

f(k)=mx+n
f(j)=tx+p
(1) The x-intercept of line k is greater than the x-intercept of line j --> 0=mx+n; 0=tx+p --> -n/m>-p/t or
n/m<p/t --> not sufficient;
(2) Lines k and j intersect at (7, 2)
2=7m+n; 2=7t+p --> 7m+n=7t+p -->not sufficient;

Combining the way you did:
n=2-7m --> n/m=2/m-7
p=2-7t --> p/t=2/t-7
n/m<p/t --> 2/m-7<2/t-7 --> 1/m<1/t --> (t-m)/mt<0
And here is the catch, from above statement you can not determine whether m>t or not. t=1<m=3 statement is true and t=1>m=-3 statement is also true.
Answer E.
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Re: xy–coordinate plane [#permalink] New post 03 Oct 2009, 12:31
Bunuel wrote:
Sorry to disappoint you guys, but seems that the answer should be E.

First of all to solve this question think that the best way is graphic approach:

We all agree that (1) and (2) alone are not sufficient.

Lets combine --> draw only X-axis. k intercept is greater than j intercept --> k intercept (k1) point right to j intercept point (j1) --> Interception of lines is above X-axis (point 7;2) --> it will give us only three possible ways to draw the lines:
A. j has negative slope, k has negative slope --> slope of k>slope of j, (because j is closer to vertical line);
B. j has positive slope, k has negative slope --> slope of k<slope of j;
C. j has positive slope, k has positive slope --> slope of k>slope of j, (because k is closer to vertical line);

So (1)+(2) not sufficient. Answer E.

BUT the way you were solving also should get E:

f(k)=mx+n
f(j)=tx+p
(1) The x-intercept of line k is greater than the x-intercept of line j --> 0=mx+n; 0=tx+p --> -n/m>-p/t or
n/m<p/t --> not sufficient;
(2) Lines k and j intersect at (7, 2)
2=7m+n; 2=7t+p --> 7m+n=7t+p -->not sufficient;

Combining the way you did:
n=2-7m --> n/m=2/m-7
p=2-7t --> p/t=2/t-7
n/m<p/t --> 2/m-7<2/t-7 --> 1/m<1/t --> (t-m)/mt<0
And here is the catch, from above statement you can not determine whether m>t or not. t=1<m=3 statement is true and t=1>m=-3 statement is also true.
Answer E.


This exactly why I said IMO E :). Thanks for explanation Bunuel! :beer
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Re: xy–coordinate plane [#permalink] New post 22 Nov 2012, 05:22
Bunuel wrote:

Lets combine --> draw only X-axis. k intercept is greater than j intercept --> k intercept (k1) point right to j intercept point (j1) --> Interception of lines is above X-axis (point 7;2) --> it will give us only three possible ways to draw the lines:
A. j has negative slope, k has negative slope --> slope of k>slope of j, (because j is closer to vertical line);
B. j has positive slope, k has negative slope --> slope of k<slope of j;
C. j has positive slope, k has positive slope --> slope of k>slope of j, (because k is closer to vertical line);



Hi Bunuel,

Request you to please look at the colored portion again and confirm if its correct. Isn't in Option A->Slope of j > Slope of K. If not, please provide your reasoning, may be I'm lacking some concept.

thanks
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Re: xy–coordinate plane [#permalink] New post 22 Nov 2012, 06:08
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imhimanshu wrote:
Bunuel wrote:

Lets combine --> draw only X-axis. k intercept is greater than j intercept --> k intercept (k1) point right to j intercept point (j1) --> Interception of lines is above X-axis (point 7;2) --> it will give us only three possible ways to draw the lines:
A. j has negative slope, k has negative slope --> slope of k>slope of j, (because j is closer to vertical line);
B. j has positive slope, k has negative slope --> slope of k<slope of j;
C. j has positive slope, k has positive slope --> slope of k>slope of j, (because k is closer to vertical line);



Hi Bunuel,

Request you to please look at the colored portion again and confirm if its correct. Isn't in Option A->Slope of j > Slope of K. If not, please provide your reasoning, may be I'm lacking some concept.

thanks


A steeper incline indicates a higher absolute value of the slope.

So, if both lines have positive slope, then the line which is steeper has greater slope.
If both lines have negative slope, then the line which is steeper has greater absolute value slope, its slope is "more negative", so less than the slope of another line.

Similar questions to practice:
if-the-slopes-of-the-line-l1-and-l2-are-of-the-same-sign-is-126759.html
slopes-of-m-and-n-124025.html
line-n-and-p-lie-in-the-xy-plane-is-the-slope-of-the-line-30553.html
lines-n-and-p-lie-in-the-xy-plane-is-the-slope-of-line-n-97007.html
in-the-xy-plane-is-the-slope-of-line-l-greater-than-the-126941.html

Hope it helps.
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Re: If lines k and j are in the xy coordinate plane, is the [#permalink] New post 27 Feb 2014, 08:13
I would solve algebraically.

Say line K is mx+b while like J is nx+c.

Question is is m>n?

Statement 1 tells us that -b/m>-c/n, but we know nothing about the signs of b and c hence insufficient.

Statement 2 says that 7m+b=7n+c, we could factorize to get m-n=c-b/7. Now question is is c-b>0? We don't know this.

Now from both statements together we still don't know whether c>b, so E is the best answer choice here.

Hope this gives a hand
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Re: If lines k and j are in the xy coordinate plane, is the   [#permalink] 27 Feb 2014, 08:13
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